How to save print-quality screenshots of the 3D view?
Have you considered the OpenGL render? You can set the resolution in the render tab, then just click the render button in the toolbar at the bottom of the 3D viewport.:



It then renders an image of the viewport (without the grid) that you can save. It also works with animation.

The render anti-aliasing settings are used so for a higher quality result you can set it to 16, since its OpenGL the additional samples are typically still quite fast to render and help to give a smoother final image.

Here's a 4K render done with the OpenGL render: